During Unit 8, you will learn about
how to use a sample statistic (such as a sample mean) to estimate the
value of a population parameter (such as the true population mean). For
example, you can estimate the true mean weight of all newborn babies in
the entire world by collecting a sample. Because the sample is only a
small portion of the entire population, errors will have to be
considered. Using a sample to create a range or interval of values that
estimates a population value is called a “confidence interval.”
The formula for calculating a 95% confidence interval for a population mean is:
Confidence Interval for Population Mean:
sample mean – E < population mean < sample mean + E
Error “E” = (1.96)*(s) / sqrt(n)
“s” is the standard deviation and “n” is the sample size.
Part 1: Confidence Intervals
Why is it often impossible to know the actual
value of any population parameter? Give an example of a population
parameter that you cannot calculate, but that you can estimate.
A sample can be used to estimate a population
parameter. How does the sample size affect the estimate? If the sample
is larger, what will this do to the error E?
Use the Confidence Interval formula above and
calculate the 95% confidence interval for any population mean of your
choice. Write down (invent) the sample size (be sure it is 30 or above),
the sample mean, and the sample standard deviation. Then, calculate the
confidence interval. Remember, you are inventing all the values, so no
two posts should look the same.
Use Excel and your invented values to calculate
the confidence interval. Include and compare the results. (Tutorials can
be found in Doc Sharing). Again, remember that your sample size must be
30 or above.